I have four socks in a drawer; each is either black or white.

Suppose that my null hypothesis is H0 : There are exactly two black socks. We decide on the following test: we take out two socks at random (all at once and without replacement). We reject H0 if the two socks are the same color. [Note: this test doesn’t make a whole lot of sense; this is just to practice the ideas.]

a) What is the significance level of this test? Explain.

b) If there are actually three black socks, what is the power of this test? Explain.

Among two independent random samples, one from city schools and one from rural schools, the
following sample statistics were computed for the amount of Instructional Spending per student
(in thousands of dollars). Assume the unknown population variances are equal to answer the
following questions.

City
Schools Rural Schools

Sample Means 5.16 5.93
Sample Sizes 35 42
Sample Variances 3.1 4.06

a. Construct a 90% confidence interval (α = 10%) for the difference between the two
sample means. Show the Margin of Error (ME) the Lower Confidence Limit (LCL) and
Upper Confidence Limit (UCL).

b. Test the null hypothesis that the two sample means are equal versus the alternative
hypothesis that the means are not equal at a 95% confidence level (α=5%). Show your
test statistic, decision criteria, and state your conclusion.

Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment​ (with magnets) group and the sham​ (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.050.05 significance level for both parts. Treatment Sham muμ mu 1μ1 mu 2μ2 n 1212 1212 x overbarx 0.480.48 0.440.44 s 0.830.83 1.381.38 a. Test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative​ hypotheses? A. Upper H 0H0​: mu 1μ1less thanmu 2μ2 The test​ statistic, t, is nothing. ​(Round to two decimal places as​ needed.) The​ P-value is nothing. ​(Round to three decimal places as​ needed.) State the conclusion for the test. ▼ Reject Fail to reject the null hypothesis. There ▼ is not is sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. Is it valid to argue that magnets might appear to be effective if the sample sizes are​ larger? Since the ▼ sample standard deviation sample mean for those treated with magnets is ▼ equal to less than greater than the sample mean for those given a sham​ treatment, it ▼ is is not valid to argue that magnets might appear to be effective if the sample sizes are larger. b. Construct a confidence interval suitable for testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. nothingless than

Here are summary statistics for randomly selected weights of newborn​ girls: nequals192​, x overbarequals27.8 ​hg, sequals7.8 hg. Construct a confidence interval estimate of the mean. Use a 90​% confidence level. Are these results very different from the confidence interval 26.5 hgless thanmuless than29.9 hg with only 14 sample​ values, x overbarequals28.2 ​hg, and sequals3.5 ​hg? What is the confidence interval for the population mean mu​? nothing hgless thanmuless than nothing hg ​(Round to one decimal place as​ needed.)

Question 35

I) Suppose that you randomly select a sample of 40 part-time journalists in January, and find that the sample pay per hour is £20.10 and the sample SD is £3.15. Compute a 95% confidence interval for the mean hourly pay of all of the part-time journalists in January, and then provide an interpretation of your interval.


II) Suppose that part-time journalists earn £17.84 per hour on average in July. Test if the data collected in Part I) suggest that the part-time journalists in January earn, on average, more than those working as part-time journalists in July. Do a hypothesis test given a 10% significance level to answer this, and then provide a conclusion.

In terms of eye colors only nine percent of humans population has blue eyes. Find the probability that out of 42 Americans at least 2 have blue eyes. I used a binomial formula?

A study was conducted on a high-pressure inlet fogging method for a gas turbine engine. Researchers considered two models. Partial output is provided below.

Answer the following questions rounding off at the nearest integer.

1. The number of observations collected for the study is equal to

2. The number of predictors considered in the reduced model is equal to

3. The F-test for global utility of the reduced model is equal to

Results suggest that the complete model provides additional information compared to the reduced model. In fact, the F-test for nested models is equal to 4.

which is greater than the rejection region F(alpha =0.05) with numerator degrees of freedom equal to 5.

and denominator degrees of freedom equal to 6.

A professor is interested in determining how difficult his exams are. He decides to examine past grades on his first exam, the content of which has remained more or less the same over the last several years. In a random sample of 15 exam scores, the sample mean was 75 with a sample standard deviation of 5. The upper bound of a 95% confidence interval for the true mean, to two decimal places, would therefore, be which of the following?

A. 77.77

B. 78.53

C. 77.17

D.73.45

E. 88.85

10. Divide the sample members into 2 groups based on marital status of the head of household.

11. Find xbar1, s1, n1 using Excel

12. Find xbar2, s2, n2 using Excel

13. Find s

Determine whether there is a difference in the mean of the quantitative variable between married and not-married households using the 2 independent samples hypothesis test. Include a screen shot of any applet you used in your calculations.

14. Choose a significance level α.

15. What is the null hypothesis Ho?

16. What is the alternative hypothesis Ha?

17. What is the test statistic t?

18. What is the corresponding p value derived from the t statistic? (Show a scree shot of how you derived the p value.)

19. What is your conclusion on the null and alternative hypothesis?

20. Explain your results in everyday language.

Q4 _CLO2 (25pts – suggested time 15 minutes): Compute the clusters for the following data (Age and Income) using k-means clustering (k=2). Use data object B and F as initial centroids. Show all the computations and the resulting clusters up to two (2) iterations.

Hints:

• Use minmax normalization to normalize your numeric attributes
• Use Manhattan distance as the dissimilarity function for numeric attributes.

Which of the following statistical tests is commonly used to test a hypothesis?

a- chi-square test

b-Student t-test

c- Z-test

d- All of the above

2) During this virus panpidemic, there has been a flurry of biotech companies working round the clock to find a vaccine for the virus. One manufacturer claims to have invented a vaccine that is 80% effective within 24-48 hours. Assume vaccine effectiveness follows a binomial distribution. A group of 100 patients are quarantined in a hospital and treated with the vaccine. a) What is the probability that 75 patients will be cured within 24-48 hours? b) What is the probability that all patients will be cured within 24-48 hours?

Use computer software packages, such as Minitab or Excel, to solve this problem.

The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

Trends in Restaurant Take-Out

A local restaurant does a pretty significant take-out business. According to the first few years that the business was open, the following table gives the percentages of take-out orders happen each day of the week.

They recently noticed that they have been short drivers some days but have been not as busy other days. In a pool of 600 orders, this is the distribution of the number of to-go orders that occurred on each day.

Test the hypothesis that the original distribution is followed at the 5% level of significance. Does the test suggest that the distribution based on recent data has changed? Show all calculations and be sure to list all important elements of the hypothesis test (Null and alternative hypotheses, critical region, test statistic, decision, and conclusion).

A movie website wants to know which movie was the best among the three parts of The Lord of The Rings and surveyed a simple random sample of 40 adults. The results are presented according to 1 = first part, 2 = second part, and 3 =third part.

2 2 3 1 1 3 3 2 3 1 1 3 3 2 2 3 1 3 3 1 2 2 1 3 1 3 3 2 1 1 2 3 2 3 3 1 1 3 2 3'

Let ? = the proportion of adults who prefer the third one.

(1) Find the sample proportion ?̂

(2) Calculate the z-statistic for the test ?0:? ≤ 0.4,??:? > 0.4.

(3) Calculate the p-value

(4) What is the conclusion of the hypothesis test? Use ? = 0.05

do step by step include original formula.